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Simplifying Powers of [tex]\(i\)[/tex]

Use the inverse relationship to complete the expression.
If [tex]\(i = \sqrt{-1}\)[/tex], then [tex]\(i^2 = \square\)[/tex]

Sagot :

GinnyAnswer
To simplify powers of [tex]\(i\)[/tex], first recall the definition of [tex]\(i\)[/tex]:

[tex]\[i = \sqrt{-1}\][/tex]

Given this definition, we can find the square of [tex]\(i\)[/tex]:

[tex]\[ i^2 = (\sqrt{-1})^2 \][/tex]

By the property of squares and square roots, we know:

[tex]\[ (\sqrt{-1})^2 = -1 \][/tex]

Thus, the simplified value of [tex]\(i^2\)[/tex] is:

[tex]\[ i^2 = -1 \][/tex]

Therefore, filling in the expression:

[tex]\[ i^2 = \boxed{-1} \][/tex]
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